Some problems in number theory (Record no. 48868)
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| 000 -LEADER | |
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| fixed length control field | 02261nam a2200241Ia 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 160627s2013||||xx |||||||||||||| ||und|| |
| 080 ## - UNIVERSAL DECIMAL CLASSIFICATION NUMBER | |
| Universal Decimal Classification number | HBNI Th50 |
| 100 ## - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Prem Prakash Pandey |
| Relator term | author |
| 245 ## - TITLE STATEMENT | |
| Title | Some problems in number theory |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Year of publication | 2013 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | 83p. |
| 502 ## - DISSERTATION NOTE | |
| Dissertation note | 2013 |
| 502 ## - DISSERTATION NOTE | |
| Degree Type | Ph.D |
| 502 ## - DISSERTATION NOTE | |
| Name of granting institution | HBNI |
| 520 3# - SUMMARY, ETC. | |
| Summary, etc | In this thesis the author has worked on three different problems. Some progress is reported on these three problems. The first problem considered is about "Higher Residue Symbols". Given a finite set S of integers, the question of finding primes p such that each integer, 'a (an element of) S' is a quadratic residue (non-residue) modulo p is dealt by various authors. Many authors including M. Fried and S. Wright have established the infinitude of primes p modulo which each "a an element of S" is a quadratic residue. The density of such primes was considered in for study. The author has generalized the problem and studied the analogous questions. The second problem considered is the Catalan's conjecture / Mihailescu's Theorem. It was conjectured by Eugene Charles Catalan in 1844 that, the only perfect powers among integers which differ by 1 are 8 and 9. As part of this thesis the author studies the equation (x)^p - (y)^q = 1 over a number field K, i.e. when x, y Elements of (O)k. Theory of 'torsion points on elliptic curves' is used to handle the equation when one of the prime is even. The chapter four formulates an appropriate Cassels criteria and prove it partially for imaginary quadratic number fields with class number one. Chapter five reports further progress made on Catalan problem considered here. The author introduces a proper obstruction group, made up of solutions of Catalan problem, and then trap it in a short exact sequence of fairly well studied objects (namely class groups and unit groups). This is pretty analogous to the work in the case of Catalan's conjecture over Z. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematics |
| 653 10 - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | HBNI Th 50 |
| 653 10 - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Number Theory |
| 720 1# - ADDED ENTRY--UNCONTROLLED NAME | |
| Thesis Advisor | Balasubramanian, R. |
| Relator term | Thesis advisor [ths] |
| 856 ## - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://www.imsc.res.in/xmlui/handle/123456789/338 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | THESIS & DISSERTATION |
| Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Full call number | Accession Number | Uniform Resource Identifier | Koha item type |
|---|---|---|---|---|---|---|---|---|
| IMSc Library | HBNI Th50 | 67764 | http://www.imsc.res.in/xmlui/handle/123456789/338 | THESIS & DISSERTATION |